Gravitational Acceleration physics lab report PDF

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General Physics I Laboratory (PHY2053L)

Gravitational Acceleration Name: Stefanie Barbulescu

Date: 09 /29 /2019

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Abstract Brief and concise statements of the major findings of the physics laboratory experiment. (5 points)

In this lab the purpose of the experiment was to find the acceleration of free-falling object near the surface of the earth. When there is no air resistance all bodies that are at the same location above the earth falling vertically have the same acceleration. The magnitude of an object is written by the symbol g with the magnitude being 9.80 m/s2 . When gravity is at a constant, the mass of the objects is M and the distance between the center of the objects would be r. Gravitational acceleration is how fast an object is falling caused by the force of gravity. While calculating this you don’t calculate the air resistance. The major findings in this lab were that you had to set up the photo gate system and drop the picket fence within its range so that it would be able to calculate the acceleration at which it fell. Measuring each bar space, it was 0.406 meters. The formulas used to calculate force are Fg = GMm/r2 . The formula that was used for acceleration was Vy= Voy-gt and the formula for time was y=Voyt-1/2gt2.

Introduction State what you show or demonstrate in this laboratory experiment. Include the background/theory and any useful equations used in the lab. (5 points)

Gravitational acceleration is an expression that is used in physics to determine the intensity of a gravitational field. It is usually expressed in meters per second squared. At the surface of the earth 1 g, is about 9.8 meters per second squared. At different points of the earth the acceleration can differ between 9.764 and 9.834. In this lab the purpose of it was to find the gravitational acceleration for when the bar is falling through the photogate system. While conducting the data, we were able to find the acceleration of the picket fence that fell within the photo gate system 50 times. The mean of the data was found by adding all of the numbers of the acceleration together and then dividing them by 50. Given that we were able to find out that the mean of the data was 9.73 while the standard deviation of the data was 0.48. The formulas that were given to us to find the force of gravity were Fg = GMm/r2 . The formula used for acceleration was Vy= Voy-gt which was used to find out how fast the picket fence fell through the photogate system.

Materials: Photogate system, picket fence and Vernier calipers. Method

1. Use the vernier caliper to measure the bar spacing. It is the width of dark and clear bar (spacing is 5.00 cm). You need to measure all bar spacing. Record your results in table 1 and calculate the average. 2. Setup the photogate system and connect it with the PASCO interface. Remember to connect PASCO interface to the computer.

Figure 1. Show the experiment setup [PASCO picket fence ME-9377A, instruction sheet]. 3. Turn on the computer and open SPARKVue on the desktop. Click on Sensor Data, then click on Settings icon . Click on “one photogate device”, then click on “one photogate and picket fence”. 4. Enter the average value of the spacing (in meter) in the “Flag Length”. 5. Select “Acceleration” only and click on “Table and Graph” icon on the right side under the “Templates”. 6. Drop the picket fence through the photogate making sure it undergoes free fall. Please do not let the picket fence hit the ground. 7. Record the value of g for 50 readings. Record your results in table 2.

Results (50 points) 2

Place your data in this section Table 1 Measurements

Bar spacing (m)

1 2 3 4 5 Average

0.0406 0.0406 0.0406 0.0406 0.0406

Table 2 Measurements 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Average- 9.73

g (m/s2) 10 9.49 10.05 8.95 9.88 9.86 9.45 10.07 8.64 9.55 9.99 9.49 10.09 9.62 9.10 9.93 9.58 10.06 9.15 9.43 10.14 9.53 10.04 9.42 8.98

Measurements 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Data Analysis (25 points) 3

g (m/s2) 9.95 9.35 10.25 8.93 9.47 9.98 9.37 10.25 8.93 10.64 10.05 9.78 10.11 9.77 9.13 9.8 10.14 10.31 9.04 10.64 9.86 10.34 10.28 9.36 10.7

This part is for data analysis. You can insert graphs and a sample of your calculation. 1. Calculate the average of the gravitational acceleration. Write your answer below. (5 points)

𝑁

∑ (𝑔 −𝑔) 2. Calculate the standard deviation (𝜎 = √ 𝑖=1 𝑖 ) of the gravitational acceleration. Write

your answer below. (5 points)

𝑁−1

2

3. Calculate the standard deviation of the mean (𝜎𝑚 = 𝜎/√𝑁) of the gravitational acceleration. Write your answer below. (5 points)

4. Write the gravitational acceleration and the standard deviation of the mean in the following format 𝑔 ± 𝜎𝑚 . (5 points)

5. The true value of the gravitational acceleration at USFSP is 9.791 m/s2. Compare between the true and experimental value of the gravitational acceleration by calculating the percent error. (5 points)

Conclusion (15 points) 4

State the main conclusion(s) in the first paragraph along with a discussion of your results. After conducting this experiment, we were able to see how gravitational acceleration is measured and how to find the time and speed it would take for the picket fence to fall through the photogate system. Using the formulas that were given we were able to find the time it took for the picket fence to drop and how long it took to pass through the photo gate system. The average time it took for the picket fence to have free fall was 9.73 meters per second squared. The length of each bar within the picket fence also had an average of about 0.0406 meters. While this experiment was conducted, we were able to find the standard deviation of the data was 0.486 meters per second squared. In the second paragraph, you must show once how your measuring tools produce a quantified experimental error and discuss its implications for your results. Using the tools that were given there could have been a quantified experimental error using the Vernier caliper. With that measuring the spaces of the bars in the picket fence, there could have been some error because if the hand on the caliper moved any bit once measuring the spaces it could have causes it to be off which then would make the data plugged into the computer slightly off. That would then cause the data when finding the acceleration using the photogate to be slightly larger or smaller than what the data was supposed to be. Another way that the tools could have produced a quantified experimental error could have been that the start button on the computer program when measuring the free fall of the picket fence could have been started later or sooner then when it was dropped which could have caused the data to be slightly off. In the third paragraph, you may discuss any other experimental errors qualitatively that may have influenced your results. Other experimental errors could have also happened while taking the data. These errors could have been that the conversion from millimeters to meters was gotten wrong or that doing the math and finding the average was calculated wrong because of having a number mistyped into your calculator or accidentally typing the same digit twice. Another way that there could have been an experimental error that would have influenced the results of the data were by using the wrong formula to calculate the force of gravity, as it could have been mistaken for the acceleration of gravity. This could have caused the data to be wrong and to be calculated as the wrong measurement.

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